Solve sqrt{(2sqrt{6})^2+(6sqrt{2})^2}

$$\sqrt { ( 2 \sqrt { 6 } ) ^ { 2 } + ( 6 \sqrt { 2 } ) ^ { 2 } }$$

Evaluate

$$4\sqrt{6}\approx 9.797958971$$

Solution Steps

Expand \left(2\sqrt{6}\right)^{2}.

$$\sqrt{2^{2}\left(\sqrt{6}\right)^{2}+\left(6\sqrt{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4\left(\sqrt{6}\right)^{2}+\left(6\sqrt{2}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\sqrt{4\times 6+\left(6\sqrt{2}\right)^{2}}$$

Multiply 4 and 6 to get 24.

$$\sqrt{24+\left(6\sqrt{2}\right)^{2}}$$

Expand \left(6\sqrt{2}\right)^{2}.

$$\sqrt{24+6^{2}\left(\sqrt{2}\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\sqrt{24+36\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{24+36\times 2}$$

Multiply 36 and 2 to get 72.

$$\sqrt{24+72}$$

Add 24 and 72 to get 96.

$$\sqrt{96}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$4\sqrt{6}$$